The height of a water column exerts the same pressure as the $70 \mathrm{cm}$ column of mercury. Will the height of the water column change if the cross-section of the water column is made wider?

The pressure of water on the ground floor is $40,000 \mathrm{Pa}$ and on the first floor is $10,000 \mathrm{Pa}$. Find the height of the first floor. (Take: density of water$=1000 \mathrm{kg} {\mathrm{m}}^{-3}$, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A simple U tube contains mercury to the same level in both the arms. If water is poured to a height of $13.6 \mathrm{cm}$ in one arm, how much will be the rise in mercury level in the other arm? 

Given: density of mercury$=13.6 \mathrm{kg} {\mathrm{m}}^{-3}$ and density of water$={10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$.

In a hydraulic machine, a force of $2 \mathrm{N}$ is applied on the piston of area of cross section $10 {\mathrm{cm}}^2$. What force is obtained on its piston of area of cross-section $100 {\mathrm{cm}}^2$?

What should be the ratio of area of cross-section of the master cylinder of a hydraulic brake so that a force of $15 \mathrm{N}$ can be obtained at each of its brake shoe by exerting a force of $0.5 \mathrm{N}$ on the  pedal?

The areas of piston in a hydraulic machine are $5 {\mathrm{cm}}^2$ and $625 {\mathrm{cm}}^2$. What force on the smaller piston will support a load of $1250 \mathrm{N}$ on the larger piston? State any assumption which you make in your calculation? 

A force $50 \mathrm{kgf}$ is applied to the smaller piston of a hydraulic machine. Neglecting friction, find the force exerted on the large piston, if diameters of the pistons are $5 \mathrm{cm}$ and $25 \mathrm{cm}$ respectively.

Two cylindrical vessels fitted with pistons A and B of area of cross-section $8 {\mathrm{cm}}^2$ and $320 {\mathrm{cm}}^2$ respectively, are joined at their bottom by a tube and, they are completely filled with water. When a mass of $4 \mathrm{kg}$ is placed on the piston A, find the pressure on piston A.

Two cylindrical vessels fitted with pistons A and B of area of cross section $8 {\mathrm{cm}}^2$ and $320 {\mathrm{cm}}^2$ respectively, are joined at their bottom by a tube and they are completely filled with water. When a mass of $4 \mathrm{kg}$ is placed on the piston A, find the pressure on piston B.